The dynamics of maps tangent to the identity and with nonvanishing index

Laura Molino
2008 Transactions of the American Mathematical Society  
Let f be a germ of a holomorphic self-map of C 2 at the origin O tangent to the identity, and with O as a nondicritical isolated fixed point. A parabolic curve for f is a holomorphic f -invariant curve, with O on the boundary, attracted by O under the action of f . It has been shown by M. Abate (2001) that if the characteristic direction [v] ∈ P(T O C 2 ) has residual index not belonging to Q + , then there exist parabolic curves for f tangent to [v]. In this paper we prove, using a different
more » ... using a different method, that the conclusion still holds just assuming that the residual index is not vanishing (at least when f is regular along [v]).
doi:10.1090/s0002-9947-08-04533-9 fatcat:nbcgvro7cjakxfanxxqtjpmgru